Jane Street–styleTraderQuantitative TraderQuestion #110
Person A and B are going to play a coin toss game. There is an initial score of 0, and whenever a head or tail appears, the score increases by 1 or decreases by 1, respectively. The coin is tossed repeatedly until one wins, that is, when the score reaches +2 or -2, A or B wins the game. There is also an initial stake of $1 for the game and person A has the option to double the stake before each coin toss. When one person wins the game, the other player needs to pay the current stake to the winner. The question is: if you are person A, what is your optimal strategy and what is your highest expected payoff in the game?
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More Jane Street–Style Trader Questions
A car has a uniformly distributed value between 0 and 1000. If you bid less than this value, you get nothing but keep your bid. If you bid more than this value, you can sell the car for 1.5 times the value. What should you bid? The surface of a 3x3 block is painted. The block is split into 27 cubes and one is dropped on the floor. What is the probability that no visible face is painted? If no visible face is painted, what is the probability that it is the center cube?You flip 4 fair coins and receive $1 for each coin that lands heads. What is the expected value of your total winnings?If you roll two dice, and you have the option to roll again and get paid the highest roll, when is it optimal to reroll?What is 2,000,000 minus 2,022?How many digits does 99 raised to the 99th power have?
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